I looked up the
BLM mission statement. Most of it is pretty reasonable, in my view. The only odd thing that was there was the very thing you pointed out, this statement: "We disrupt the Western-prescribed nuclear family structure requirement by supporting each other as extended families and “villages” that collectively care for one another, especially our children, to the degree that mothers, parents, and children are comfortable. "
Now, it's not all that specific what is exactly meant there. I don't know that it is saying that children should be raised without a father, and I would bet that isn't what is intended. It seems to me what it is saying that it takes a village to raise a child, and that larger society has duty in raising its citizens, at least if they want those citizens to be well-balanced. I don't disagree with that notion, however I do disagree with the notion that fathers aren't important. But it should be kept in mind that families can take all kinds of forms, and just because some families do not have the traditional one-father one-mother structure doesn't necessarily mean they are worse off.
Something else to keep in mind, it seems to me that BLM isn't as centralized as one web page or one organization. The fact that so many cities had such large protests so quickly speaks to the vitality and legitimacy of the root cause of Black Lives Matter, which is also the main thrust of the mission statement, that Black Americans are unfairly targeted by police and the justice system.
I can't watch those Youtube videos at the moment since I am not at a computer that has sound playback capability.